Admissibility and generalized nonuniform dichotomies for discrete dynamics

TL;DR

This paper characterizes nonuniform dichotomies in discrete dynamics using admissibility conditions, extends robustness results, and unifies various types of dichotomies including exponential, polynomial, and logarithmic growth cases.

Contribution

It provides a unified framework for characterizing nonuniform dichotomies via admissibility and derives robustness results, covering several growth types.

Findings

Characterizations of nonuniform dichotomies based on admissibility.

Robustness results for various nonuniform dichotomies.

Recovery of known results and new insights for logarithmic growth cases.

Abstract

We obtain characterizations of nonuniform dichotomies, defined by general growth rates, based on admissibility conditions. Additionally, we use the obtained characterizations to derive robustness results for the considered dichotomies. As particular cases, we recover several results in the literature concerning nonuniform exponential dichotomies and nonuniform polynomial dichotomies as well as new results for nonuniform dichotomies with logarithmic growth.